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If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 5 ho

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Question: If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 5 hours, how long will it take to fill the tank if both pipes are opened together?

Options:

  1. 1.5 hours
  2. 2 hours
  3. 2.5 hours
  4. 3 hours

Correct Answer: 2.5 hours

Solution: 

The combined rate is (1/3 - 1/5) = (5-3)/15 = 2/15. Therefore, it will take 15/2 hours or 7.5 hours.

If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 5 ho

Practice Questions

Q1
If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 5 hours, how long will it take to fill the tank if both pipes are opened together?
  1. 1.5 hours
  2. 2 hours
  3. 2.5 hours
  4. 3 hours

Questions & Step-by-Step Solutions

If a tank can be filled by a pipe in 3 hours and emptied by another pipe in 5 hours, how long will it take to fill the tank if both pipes are opened together?
  • Step 1: Determine the rate at which the filling pipe works. If it fills the tank in 3 hours, its rate is 1 tank per 3 hours, or 1/3 of the tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. If it empties the tank in 5 hours, its rate is 1 tank per 5 hours, or 1/5 of the tank per hour.
  • Step 3: Calculate the combined rate when both pipes are open. This is done by subtracting the emptying rate from the filling rate: (1/3 - 1/5).
  • Step 4: To subtract the fractions, find a common denominator. The common denominator for 3 and 5 is 15.
  • Step 5: Convert the rates to have the common denominator: (1/3 = 5/15) and (1/5 = 3/15).
  • Step 6: Now subtract the two rates: (5/15 - 3/15 = 2/15). This means together, the pipes fill 2/15 of the tank in one hour.
  • Step 7: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 divided by (2/15) equals 15/2 hours.
  • Step 8: Simplify 15/2 hours to get 7.5 hours.
  • Rate of Work – Understanding how to calculate the rate at which work is done when multiple processes are involved.
  • Combined Rates – Learning to combine rates of filling and emptying to find the net effect on the tank's fill level.
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